1. Field of the Invention
The present invention relates to a semiconductor device including a stress detector, and more particularly, it relates to means for improving a temperature characteristic of the stress detector and means for correcting variations in sensitivity of several stress detectors in different semiconductor devices, both of which utilize a piezo resistance effect of semiconductor.
2. Description of the Prior Art
A conventional semiconductor device having a stress transducer will be explained with reference to FIGS. 18 and 19. FIGS. 18(a) and 18(b) are a plan view and a side view showing a pressure sensor for as an exemplary semiconductor device. As can be seen, the pressure sensor includes a substrate A for the pressure sensor, peripheral circuit areas ar1 to ar4 formed on the substrate A, a diaphragm ar5 which is transformed by an external pressure to develop stress, strain gauge resistances S1 to S4 which are formed in the diaphragm ar5 and utilize a piezo resistance effect to transduce a variation in the stress of the diaphragm ar5 into a variation in resistance value. The pressure sensor has a bridge circuit consisting of the strain gauge resistance S1 to S4 so as to act as a pressure detector. Reference symbol P designates pressure applied to the pressure sensor.
FIG. 19 is a circuit diagram showing a conventional semiconductor device having a stress transducer which includes a stress detector 1 (e.g., a presure detector for a pressure sensor) which utilizes a piezo resistance effect of semiconductor, and strain gauge resistances 2a, 2b, 2c and 2d of which the stress detector 1 is comprised. For example, strain gauge resistances S1 to S4 shown in FIG. 18 are examples of the strain gauge resistances 2a to 2d. Such strain gauge resistances 2a to 2d are ordinarily made by impurity diffusion. Reference symbol 3a is a node between the strain gauge resistances 2c and 2d while 3b is a node between the strain gauge resistances 2a and 2b, and voltage developed between the nodes 3a and 3b is in proportion to a stress to be detected (e.g., a stress developed because of a transformation of the diaphragm in accordance with a pressure in the pressure sensor, and so forth). The semiconductor device having a stress transducer further includes an operational amplifier 4 for amplifying output voltage V.sub.span (differential voltage between the nodes 3a and 3b) of the stress detector 1, resistances 5, 6, 7 and 8 for determining an amplification factor of the operational amplifier 4, grounds 9 to which one of terminals of the resistance 8, etc. are grounded, an output terminal 10 of the operational amplifier 4, a power source 11 for supplying voltage V.sub.CC which is used for activating the stress detector 1, a resistance 12 connected between the power source 11 and a node 3c, an operational amplifier 13 having its output terminal connected to a node 3d of the stress detector 1, a non-inversion input terminal 14 of the operational amplifier 13, an inversion input terminal 15 of the operational amplifier 13, a resistance 16 connected between the power source 11 and the non-inversion input terminal 14, and a resistance 17 having its one terminal grounded and the other terminal connected to the non-inversion input terminal 14.
Next, an operation of the semiconductor device will be described. Assuming now that resistance values of the strain gauge resistances 2a, 2b, 2c and 2d are R.sub.Ga, R.sub.Gb, R.sub.Gc, and R.sub.Gd, potentials at the nodes 3a and 3b are E.sub.3a and E.sub.3b, and potentials at the nodes 3c and 3d are E.sub.3c and E.sub.3d, E.sub.3a and E.sub.3b are expressed with the potentials E.sub.3c and E.sub.3d at the nodes 3c and 3d, as follows: ##EQU1##
With the output voltage V.sub.span of the stress detector 1, the formulas (1) and (2) lead to the following formula: ##EQU2## under the condition that no stress is applied to the strain gauge resistances 2a, 2b, 2c and 2d of the stress detector 1 (generally, the stress to be detected is zero). For example, stress P applied to a pressure sensor is zero (vacuum), the strain gauge resistances 2a, 2b, 2c and 2d are arranged so as to satisfy R.sub.Ga =R.sub.Gb =R.sub.Gc =R.sub.Gd =R.sub.GO as to the resistance values of the strain gauge resistances 2a to 2d, the output voltage V is shown as follows: ##EQU3##
Then, with a stress applied to the stress detector 1 (e.g., pressure is applied to the pressure sensor, or the like), the strain gauge resistances 2a, 2b, 2c and 2d have their respective resistance values varied because of a piezo resistance effect. Assuming that a variation amount is .DELTA.R.sub.G, an adequate arrangement of the strain gauge resistances 2a, 2b, 2c and 2d enables a polarity (positive or negative) of .DELTA.R.sub.G to be arbitrarily selected. For example, the strain gauge resistances 2a, 2b, 2c and 2d are appropriately arranged with the strain gauge resistances 2a and 2d positive in polarity and the strain gauge resistances 2b and 2c negative in polarity, the strain gauge resistances, when a certain pressure is applied thereto, assume their respective resistance values R.sub.Ga to R.sub.Gd as in the following formula: EQU R.sub.Ga =R.sub.GO +.DELTA.R.sub.G EQU R.sub.Gb =R.sub.GO -.DELTA.R.sub.G EQU R.sub.Gc =R.sub.GO -.DELTA.R.sub.G EQU R.sub.Gd =R.sub.GO +.DELTA.R.sub.G ( 5)
Then, substituting the formula (5) for the formula (3), the following formula is given: ##EQU4##
As is obvious from the formula (6), the output voltage V.sub.span of the stress detector 1 is in proportion to .DELTA.R.sub.G when (E.sub.3c -E.sub.3d) is constant because R.sub.GO is constant. In other words, output voltage in proportion to the stress applied to the strain gauge resistances 2a, 2b, 2c and 2d is developed.
If .DELTA.R.sub.G is constant, also the output voltage V.sub.span is in proportion to (E.sub.3c -E.sub.3d). Thus, arbitrary sensitivity of the stress detector 1 can be chosen by varying (E.sub.3c -E.sub.3d).
It is generally known that when the strain gauge resistances 2a, 2b, 2c and 2d are formed by impurity diffusion in semiconductor, a resistance changing rate (.delta.R.sub.GO /.delta.F (where .delta. expresses partial differential)) in accordance with the stress F applied to the strain gauge resistances 2a, 2b, 2c and 2d is in proportion to a piezo resistance coefficient. The piezo resistance coefficient exhibits a great temperature dependency, and it also depends upon the kind of the semiconductor where impurity is diffused, a crystal orientation of the resultant strain gauge resistance, and a concentration of diffused impurity. Hence, fixing a manufacturing method and a structure of elements in contrast with the above, a temperature characteristic of the piezo resistance coefficient becomes stable with a temperature coefficient of a fixed value. Transforming the formula (6) with the piezo resistance coefficient, the following formula is given: EQU V.sub.span (T)=a.multidot.F.multidot..pi.(T).times.(E.sub.3c E.sub.3d) (7)
In the formula (7), a is a proportionality constant, F is a stress, .pi.(T) is a piezo resistance coefficient, and T is a temperature of the stress detector 1.
Now, with the temperature coefficient .alpha. of the piezo resistance coefficient, the following formula is given: ##EQU5##
Specifically, the piezo resistance coefficient has a negative temperature coefficient, and as the temperature rises, the piezo resistance coefficient .pi. becomes small. The formula (7) is transformed with the formula (8) as follows: ##EQU6##
As has been described, the output voltage V.sub.span of the stress detector 1 is in proportion to the stress F applied to the strain gauge resistances 2a, 2b, 2c and 2d and the voltage (E.sub.3c -E.sub.3d) applied to the stress detector 1, and in inverse proportion to the temperature T of the stress detector 1.
The output voltage V.sub.span of the stress detector 1 is a differential voltage, and for the purpose of single-ending it for convenience in use, it is differentially amplified by the operational amplifier 4. Assuming that resistance value of the resistances 5, 6, 7 and 8 are R.sub.5, R.sub.6, R.sub.7 and R.sub.8, respectively, output voltage V.sub.out developed at the output terminal 10 of the operational amplifier 4 can be expressed as follows: ##EQU7##
If R.sub.5 =R.sub.7 and R.sub.6 =R.sub.8, the following formula is given: ##EQU8##
In accordance with the formula (11), the differential voltage V.sub.span is single-ended by the operational amplifier 4 and so forth, and the voltage V.sub.span is further amplified to (R.sub.6 /R.sub.5) times.
As the output voltage V.sub.span of the stress detector is in inverse proportion to the temperature T of the stress detector 1 as expressed in the formula (9), it is necessary to utilize peripheral circuits of the stress detector 1 to correct the inverse proportion characteristic to the temperature T so that an accuracy of the stress detector 1 can be enhanced. This is implemented by using the resistance 12 and the operational amplifier 13.
Assuming that the resistances 12, 16 and 17 have respective resistance values R.sub.12, R.sub.16 and R.sub.17, potential E.sub.14 at the non-inversion input terminal 14 of the operational amplifier 13 is given by the following formula: ##EQU9##
In this formula, V.sub.cc is a voltage between a potential of the power source 11 and the ground. Then, the potential E.sub.3c is given by the following formula: ##EQU10##
Thus, current I.sub.G flowing in the resistance 12 is given by the following formula: ##EQU11##
The current I.sub.G flows in a bridge circuit, and therefore, there is a relation as expressed in the following formula: EQU E.sub.3c -E.sub.3d =R.sub.GO .multidot.I.sub.G ( 15)
Substituting the formulas (9), (14) and (15) for the formula (11), the following formula is given: ##EQU12##
The stress detector 1 has its specific proportional constant a, and in order to coordinate its variations in constant of several stress detectors in different semicoonductor devices, any of the R.sub.5, R.sub.6, R.sub.12, R.sub.16 and R.sub.17 may be adjusted. Conventionally, however, the resistance R.sub.17 is generally adjusted. R.sub.GOO is the resistance value R.sub.GO at the reference temperature while T is equal to a difference between an environmental temperature and the reference temperature. For instance, R.sub.GOO is the resistance value at 0.degree. C. and T is an environmental temperature expressed in .degree. C.
The strain gauge resistances 2a, 2b, 2c and 2d have a positive temperature coefficient B because they are made by the impurity diffusion into semiconductor. Thus, the resistance value R.sub.GO of the strain gauge resistances 2a to 2d is expressed as follows: EQU R.sub.GO =R.sub.GOO .times.(1+.beta..multidot.T) (17)
Substituting the formula (17) for the formula (16), the following is obtained: ##EQU13##
As will be recognized from the formula (18), if the resistance 12 has no temperature dependency, and setting impurity concentrations of the strain gauge resistances 2a, 2b, 2c and 2d so as to satisfy .alpha.=.beta., the output voltage V.sub.out no longer depends upon a temperature. Even if the resistances 5, 6, 7 and 8 are also made by the impurity diffusion into semiconductor and have respective temperature dependencies, they are cancelled by one another if they are identical in temperature coefficient. Similarly, the resistances 16 and 17 can be cancelled by each other if they are identical in temperature coefficient.
Thus, choosing appropriate impurity concentrations of the strain gauge resistances 2a, 2b, 2c and 2d, the temperature coefficient .beta. of the resistance value R.sub.GO of the strain gauge resistances 2a to 2d is equal to the temperature coefficient .alpha. of the piezo resistance coefficient .pi., and using the resistance 12 of a small temperature coefficient and appropriately adjusting the resistances 16 and 17, a temperature characteristic of the stress detector 1 and variations in sensitivity among several stress detectors in different semiconductor devices are corrected, so that a semiconductor device with high accuracy can be obtained.
Since the conventional semiconductor device is configured as mentioned above, the temperature coefficient .beta. of the strain gauge resistances 2a, 2b, 2c and 2d must be set so as to be equal to the temperature coefficient .alpha. of the piezo resistance coefficient .pi., and this is very difficult. Also, since the resistance R.sub.12 of a small temperature coefficient is required for producing a constant current I.sub.G which is not affected by temperature, the resistance R.sub.12 is formed of a thin film resistance, for example. This brings great obstacles to form a semiconductor device including the strain gauge resistance 2a to 2d of diffusion resistances and the thin film resistance R.sub.12 on a single semiconductor chip; e.g., a manufacturing process of the semiconductor is device is complicated.